In general, stereo-correlation methods require at least two capturing cameras making it possible to capture images of the object to be measured from two different angles and means for analyzing and processing the images output by these two cameras. The measurement principle is illustrated in FIG. 1. The surface of an object O is represented by a set of points M with coordinates (x,y,z) in a reference frame (X, Y, Z) linked to the object. In the reference frame (U1, V1) of the image plane of the first camera, the image of the point M is at M1 with coordinates (u1, v1) and in the reference frame (U2, V2) of the image plane of the second camera, the image of the point M is at M2 with coordinates (u2, v2). Knowing the two transfer matrices between the reference frame (X, Y, Z) and the reference frames (U1, V1) and (U2, V2), it is then possible to find the coordinates of each point M of the object, knowing the coordinates of its two projections M1 and M2 in the image planes of the two cameras.
To the extrinsic parameters that are these changes in reference frame are added intrinsic quantities such as the focal lengths of the lenses of the cameras, the scale parameters or else the coordinates of the focal points that characterize each of the image capturing means used. These two sets of parameters must be known in order to be able to reconstruct the three-dimensional surface shapes of the object. Note that the two sets of parameters can be grouped to define the transfer matrix associated with each camera; the latter being determined without necessarily having to distinguish between the intrinsic and extrinsic parameters.
Stereo-correlation methods include two main steps which are on the one hand a calibration step and on the other hand a spatial matching step enabling the determination of the geometrical features of the measured object. These first two steps can be followed by a third step of tracking the geometrical features over time. The latter step is useful when the object undergoes processing likely to induce deformation, for example when the object is subject to a mechanical strength test or during a manufacturing or assembly method.
As seen in the previous paragraph, it is essential to have full knowledge of the link existing between the reference frame of the object and the reference frame of the image planes of the two cameras. To perform this calibration step, a template—a three-dimensional calibration test pattern, the geometry of which is fully known—is used. By way of example, FIG. 2 represents the calibration of the image plane of the camera 1. The calibration test pattern ME is composed of one or of two planar surfaces forming a known angle between themselves. Each surface is covered with distinctive black and white geometrical shapes which can be rectangles or discs, for example. The test pattern in FIG. 2 is thus covered with a black and white checkerboard pattern.
In the example in FIG. 2, three points on the checkerboard pattern P1, P2 and P3 of known position give three projected images I1, I2 and I3 of known position in the image plane of the camera 1. It has been demonstrated that at least eight calibration points are required to obtain a calibration of the measurement system, i.e. the determination of the elements of the transfer matrices. The camera lenses not being fully alike and including optical aberrations, the calibration phase can also introduce aberration corrections for each camera and then requires a larger number of measurement points. This phase is, of necessity, complex if a high accuracy of measurement is desired within a given volume of measurement.
The function of the spatial matching step consists in finding in the two image planes the two projection points M1 and M2 corresponding to one and the same object point M. These points being determined, it is then possible to retrieve the three-dimensional coordinates of the point M. Various methods are implemented to perform this matching. They are based on a Digital Image Correlation code, also known by the acronym “DIC”.
Various types of DIC code exist. A first type consists in performing local correlations between the two images of one and the same object so as to detect for a point M1 belonging to the first image plane the corresponding point M2 in the second image. To perform this correlation, the images are divided into “thumbnails” of small dimensions. Thus, a thumbnail can be a square, consisting of 16×16 pixels for example. For a first determined thumbnail belonging to the first image plane, the second corresponding thumbnail is sought in the second image plane. Given that the thumbnails are of small dimensions, it is possible to consider that the second thumbnail is obtained by a simple transform of the first thumbnail, i.e. a translation, and often a displacement of constant gradient on the thumbnail, or optionally more complex transforms. In this way the correlation computations are greatly simplified, taking into account the local nature of the analysis. However, this method, by its very nature, does not take into account transforms more complicated than those used in the analysis but which are likely to exist between the two thumbnails. In addition, the regularity of the displacement field, which translates, for example, into the continuity, or differentiability existing between contiguous thumbnails, is not taken into account.
It will be understood that, to obtain a high spatial resolution, the dimensions of the thumbnails are reduced, but in doing so, the correlation becomes more sensitive to noise and the determination of the transfer matrices becomes more uncertain.
A second type of DIC code consists in performing a global correlation between the two images. In this case, an attempt will be made to determine the whole displacement field existing between the two images so as to obtain the smallest possible difference between the two images. To perform this step, it is considered that the two images are described by gray level variations, which are a function of the spatial coordinates captured in the two image planes. These two images are denoted ƒ(x) and g(x), x representing the coordinates of the points belonging to the two images. It is then considered that the second image is equal to the first image to within a displacement field denoted u(x). The following equation is obtained:ƒ(x)=g[x+u(x)]  Relationship 1
The displacement field u(x) is determined by minimizing over the whole volume of the object the quadratic difference existing between the two sides of relationship 1, the displacement field being decomposed over a basis of suitable functions.
For more information on this method, the reader is referred, in particular, to a first article entitled ““Finite-element” displacement fields analysis from digital images: Application to Portevin-Le Châtelier bands”, published in “Experimental Mechanics 46 (2006) 789-804” by Gilles Bernard, François Hild and Stéphane Roux and also to a second article entitled “Characterization of necking phenomena in high speed experiments by using a single camera”, published in “EURASIP Journal on Image and Video Processing 2010 (2010) 215956” by Gilles Bernard, Jean-Michel Lagrange, François Hild, Stéphane Roux and Christophe Voltz. In these two articles, the first on DIC, the second on its use in the context of stereo-correlation, the kinetic field basis chosen for the decomposition of the displacement field are the Q4P1 shape functions of a regular square mesh.
This global correlation method requires greater computing means than the former but offers superior accuracy.
However, even if they perform for users in a way that is satisfactory overall, these methods have certain drawbacks. These notably include a certain complexity of the calibration phase, measurement results in the form of clusters of points that it is then necessary to reshape, the need to rely on filtering or projection without being able to judge and quantify the loss of accuracy entailed, a certain sensitivity to measurement noise and, finally, difficulty in assessing the quality of the measurement obtained in the absence of any reference.
These difficulties stem partly from the fact that the measurements are made a priori, with no prior knowledge of the shape and the geometry of the object. However, today, the very large majority of industrial objects are designed and produced based on computer-assisted design software programs, also known as Computer Aided Design, known by the acronym CAD. A parametric representation of the object to be measured is therefore naturally available. The core of the stereo-correlation method according to the invention is the use of this parametric representation either during the calibration step, or during the measurement step, or during both, the object to be measured being its own template. By its very nature, the method according to the invention is akin to global correlation DIC codes.